Algebra Examples

$\sqrt{72 a^{3}} b^{4} c^{5}$

Step 1

Rewrite $72 a^{3}$ as ${(6 a)}^{2} \cdot (2 a)$ .

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Step 1.1

Factor $36$ out of $72$ .

$\sqrt{36 (2) a^{3}} b^{4} c^{5}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 a^{3}} b^{4} c^{5}$

Step 1.3

Factor out $a^{2}$ .

$\sqrt{6^{2} \cdot 2 (a^{2} a)} b^{4} c^{5}$

Step 1.4

Move $2$ .

$\sqrt{6^{2} a^{2} \cdot 2 a} b^{4} c^{5}$

Step 1.5

Rewrite $6^{2} a^{2}$ as ${(6 a)}^{2}$ .

$\sqrt{{(6 a)}^{2} \cdot 2 a} b^{4} c^{5}$

Step 1.6

Add parentheses.

$\sqrt{{(6 a)}^{2} \cdot (2 a)} b^{4} c^{5}$

$\sqrt{{(6 a)}^{2} \cdot (2 a)} b^{4} c^{5}$

Step 2

Pull terms out from under the radical.

$6 a \sqrt{2 a} b^{4} c^{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$